1. Field of the Invention
The present invention relates to a parameter extracting method. More particularly, the present invention relates to an extracting method of a proximity effect correction parameter used for charged particle beam exposure using electron beams.
2. Description of the Related Art
At present, direct drawing exposure by electron beams is used as one of key technologies in producing engineering samples for mass-production of semiconductor devices. When performing exposure using a mask, reedition is often performed particularly in design of multilayer wiring layers. Therefore, the EB direct drawing exposure technology capable of performing exposure without using a mask is extremely effective in view of cost or TAT (Turn Around Time).
It is generally known that in the electron beam exposure, a resolution line width changes depending on a density of an exposure pattern due to a proximity effect. Therefore, influences of the proximity effect are calculated based on the EID (Exposure Intensity Distribution) function to perform the proximity effect correction for optimizing an exposure amount to or size of each pattern so that the same absorbed energy can be finally obtained in each pattern. For example, when a resist in which a pattern is formed is formed on a substrate composed of a single material, the EID function can be empirically represented by the following formula (1):
                              f          ⁡                      (                          x              ,              y                        )                          =                              1                          π              ⁡                              (                                  1                  +                  η                                )                                              ⁢                      {                                                            1                                      β                    f                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    x                            2                                                    +                                                      y                            2                                                                                                    β                          f                          2                                                                                      )                                                              +                                                η                                      β                    b                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    x                            2                                                    +                                                      y                            2                                                                                                    β                          b                          2                                                                                      )                                                                        }                                              (        1        )            
In the formula (1), βf is a forward scattering length, η is a backward scattering ratio and βb is a backward scattering length. A first term represents a forward scattering intensity distribution and a second term represents a backward scattering intensity distribution. Forward scattering has a large effect on a narrow range. On the contrary, backward scattering has a relatively small effect on a wide range. The backward scattering ratio η is a ratio of a value obtained by integrating influences of the backward scattering in a specific region to that of the forward scattering.
In order to form a pattern having high dimensional accuracy, the selection of βf, η and βb of the formula (1) is important. Conventionally, also a method for extracting the βf, η and βb most suitable for the proximity effect correction is proposed (see, e.g., Japanese Unexamined Patent Application Publication No. 2003-218014).
In recent years, when actually performing electron beam exposure, a multitiered structure comprised of various materials, such as a wiring layer or a contact hole layer is formed under a resist in many cases. For example, when forming the wiring layer, Al or Cu is used for a wiring and SiO2 is used between wirings. Further, when forming the contact hole layer, W or Cu is used for a via and SiO2 is used between vias.
A heavy metal typified by W is easy to reflect electrons and therefore, is difficult for electrons to be transmitted. On the other hand, a relatively light substance such as Al or SiO2 reflects a small number of electrons and therefore, is easy for electrons to be transmitted. Accordingly, even within the same layer, a scattering state of electrons considerably varies depending on the types of materials constituting the layer. Further, an electron transmitted through a layer enters a lower layer. Also in the lower layer, the scattering state of electrons varies depending on the types of materials constituting the layer. On the other hand, also in a process where an electron which deeply enters returns to a resist, the electron is reflected by a heavy metal within a halfway layer (a screening effect) and therefore, the number of electrons that reach the resist is extremely reduced, as compared with a case where a heavy metal is absent.
As described above, the scattering state of electrons in the multitiered structure is extremely complicated. Therefore, the proximity effect cannot be simply estimated by using the EID function of the formula (1). More specifically, in the case of the multitiered structure, an influence of the backward scattering actually varies depending on a combination of layers constituting the structure. In spite of the fact, when using the formula (1) excluding the combination of layers, the backward scattering intensities are computationally equalized irrespective of the combination of the layers.
On the other hand, also a technique for calculating an influence of the backward scattering while considering the combination of the layers under the resist is conventionally proposed (see, e.g., Japanese Unexamined Patent Application Publication No. 2005-101501). This proposal is as follows. That is, in each of the layers, a parameter such as a reflection coefficient, a transmission coefficient or a diffusion length is defined for each of the construction materials of the layers. Further, weighing is performed using an area density (a share) of each construction material to calculate a stream of electrons within the layers, in other words, a stream of energy.
FIG. 15 illustrates a principle of a conventional calculation technique of the backward scattering intensity.
As shown in FIG. 15, the following case is supposed. That is, on a substrate (a zeroth layer), (N−1) layers (from a first layer to an (N−1)th layer) are sequentially laminated and then, a resist (an Nth layer) as an uppermost layer is formed. Further, a stream of energy (a stream of electrons) is herein considered as follows.
As indicated by arrows in FIG. 15, electrons of energy (or the number of electrons) EN are first transmitted through the resist to enter an (N−1)th layer. Among them, electrons of energy EN−1 corresponding to a transmission coefficient TN−1 are transmitted through the (N−1)th layer to enter an (N−2)th layer, and electrons of energy EN−1′ corresponding to a reflection coefficient RN−1 are reflected from the (N−1)th layer to return to the resist. Further, among electrons of energy EN−1, which are transmitted through the (N−1)th layer to enter the (N−2)th layer, electrons of energy EN−2 corresponding to a transmission coefficient TN−2 of the (N−2)th layer are transmitted through the (N−2)th layer to enter an (N−3)th layer, and electrons of energy EN−2′ corresponding to a reflection coefficient RN−2 of the (N−2)th layer are reflected from the (N−2)th layer. Thus, among electrons of energy E2, which are transmitted through the second layer to enter the first layer, electrons of energy E1 corresponding to a transmission coefficient T1 of the first layer are transmitted through the first layer to enter the substrate, and electrons of energy E1′ corresponding to a reflection coefficient R1 of the first layer are reflected from the first layer. Further, among electrons of energy E1, which are transmitted through the first layer to enter the substrate, electrons of energy E0′ corresponding to a reflection coefficient R0 of the substrate are reflected from the substrate.
On the other hand, among electrons of energy E0′, electrons of energy E1″ corresponding to the transmission coefficient T1 of the first layer are transmitted through the first layer to enter the second layer. On this occasion, electrons of energy E1″ as well as electrons of energy E1′, which are reflected from the first layer, enter the second layer. Similarly, electrons of energy EN−2″, which are transmitted through the (N−2)th layer, as well as electrons of energy EN−2′, which are reflected from the (N−2)th layer, enter the (N−1)th layer. Finally, electrons of energy EN−1″ corresponding to the transmission coefficient TN−1, which are transmitted through the (N−1)th layer, as well as electrons of energy EN−1′ corresponding to the reflection coefficient RN−1, which are reflected from the (N−1)th layer, return to the resist.
Based on the stream of energy as described above, calculation is recursively performed from the uppermost layer to the lowermost layer, and the energy which finally returns to the resist is qualified as energy absorbed in the resist by the backward scattering. In this calculation technique, a transmission coefficient or reflection coefficient of each construction material is used to add reflection, transmission or screening effects of electrons, which are produced by each construction material of each layer. Therefore, the backward scattering intensity can be accurately calculated.
When calculating the backward scattering intensity of the multitiered structure using the above-described technique to perform proximity effect correction, the parameters such as a reflection coefficient, transmission coefficient or diffusion length of each construction material of each layer must be accurately extracted. These parameters are normally extracted using actual exposure results and calculation results. Further, the proximity effect correction of the objective pattern is performed using the thus obtained parameters. Then, exposure through the pattern is performed according to the correction.
However, in the case of the multitiered structure, numerous combinations of the layers are possible. Therefore, a long period of time is required for a work operation of experimentally performing exposure for all the combinations and extracting a parameter using the exposure result. For example, in the case of a three-layer structure where each layer is composed of two types of materials such as a W plug and an insulating film, when changing a share of the W plug in ten ways, 10×10×10=1000 combinations of the layers are possible. Further, the number of experimental data used for extracting each parameter becomes huge depending on the types of exposure patterns, for example, depending on the share or existing range of the pattern.